Question 1172902: In a class of 50 students 24 like football 21 basketball and cricket six like football and basketball 3 like basketball only, five like all three games, and 14 did not like any of the three games.
1.illustrate this information of Venn diagram
2. Find the number of students who like
A. Football and cricket
B. Exactly one of the game
C. Exactly two of the game.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Absolutely, let's solve this problem step-by-step using a Venn diagram.
**1. Venn Diagram**
Let's use the following notation:
* F = Football
* B = Basketball
* C = Cricket
We are given:
* Total students = 50
* n(F) = 24
* n(B) = 21
* n(F ∩ B) = 6
* Students who like basketball DISABLED_event_only= 3
* n(F ∩ B ∩ C) = 5
* Students who like none of the games = 14
Here's how we'll build the Venn diagram:
1. **Start with the intersection of all three:**
* n(F ∩ B ∩ C) = 5. Place 5 in the center of the Venn diagram where all three circles overlap.
2. **Football and Basketball:**
* n(F ∩ B) = 6. We know 5 like all three, so 6 - 5 = 1 student likes only football and basketball. Place 1 in the F ∩ B region.
3. **Basketball Only:**
* 3 students like only basketball, place a 3 in the B only section of the venn diagram.
4. **Basketball circle:**
* We know n(B)=21. We have 5+1+3=9 of those students accounted for. 21-9=12. We do not yet know how many of those 12 like cricket, so we will fill in the values that we can.
5. **Students who like none:**
* 14 students like none of the games. Place 14 outside the circles.
6. **Total within the circles:**
* 50 total students - 14 who like none = 36 students who like at least one sport.
7. **Football circle:**
* n(F) = 24. We know 5+1=6 of those. 24-6=18. 18 students like football and cricket, or football only. We cannot yet determine the individual values.
8. **Cricket values:**
* We can find the total amount of students that like cricket. 36 students total like at least one sport. 36 - 3 - 1 - 5 - 18 = 9. 9 students like cricket only or cricket and football. We cannot yet determine the individual values.
9. **Completing the diagram:**
* We know that the remaining students that like basketball must total 12. Let x= the students that like basketball and cricket only. 12 = x+5. x=7. 7 students like Basketball and Cricket only.
* We know the students that like cricket total 9+7+5 = 21.
* We know that the football only students equal 24-1-5-students that like football and cricket only. 24-6-cricket and football DISABLED_event_only= football only. 21-5-7=9. 9 students like cricket only. 24-1-5 = 18. 21-9-5-7=0. 18-0=18. 18 students like football only.
* The Venn diagram is complete.
**2. Answers**
**A. Football and Cricket:**
* To find the number of students who like football and cricket, we add the students who like only football and cricket (0) and those who like all three (5): 0+5=5.
* 5 students like football and cricket.
**B. Exactly One Game:**
* Add the number of students who like only football (18), only basketball (3), and only cricket (9): 18 + 3 + 9 = 30.
* 30 students like exactly one game.
**C. Exactly Two Games:**
* Add the number of students who like football and basketball only (1), basketball and cricket only (7), and football and cricket only (0): 1 + 7 + 0 = 8.
* 8 students like exactly two games.
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
In a class of 50 students, 24 like football, 21 basketball and cricket, six like football and basketball,
3 like basketball only, five like all three games, and 14 did not like any of the three games.
1.illustrate this information of Venn diagram
2. Find the number of students who like
A. Football and cricket
B. Exactly one of the game
C. Exactly two of the game.
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The solution to this problem in the post by @CPhill is INCORRECT.
The error is that @CPhill incorrectly reads/interprets the problem.
Indeed, when retelling what are given, he writes n(B) = 21, and then uses it in his solution.
It is INCORRECT. n(B) = 21 is NOT given.
What is given in the problem is n(B∩ C) = 21.
Therefore, everything what follows in the post by @CPhill is irrelevant and incorrect.
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Regarding the post by @CPhill . . .
Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.
The artificial intelligence is like a baby now. It is in the experimental stage
of development and can make mistakes and produce nonsense without any embarrassment.
It has no feeling of shame - it is shameless.
This time, again, it made an error.
Although the @CPhill' solutions are copy-paste Google AI solutions, there is one essential difference.
Every time, Google AI makes a note at the end of its solutions that Google AI is experimental
and can make errors/mistakes.
All @CPhill' solutions are copy-paste of Google AI solutions, with one difference:
@PChill never makes this notice and never says that his solutions are copy-past that of Google.
So, he NEVER SAYS TRUTH.
Every time, @CPhill embarrassed to tell the truth.
But I am not embarrassing to tell the truth, as it is my duty at this forum.
And the last my comment.
When you obtain such posts from @CPhill, remember, that NOBODY is responsible for their correctness,
until the specialists and experts will check and confirm their correctness.
Without it, their reliability is ZERO and their creadability is ZERO, too.
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